I'd be very tempted to discuss it with a reasonably senior manager within your office: that is, after all, their job - to manage stuff...
Collecting for charity and then keeping the money is Fraud, a serious criminal offence, and if she has used your departmental facilities - work email, time, premises etc.. to attempt to legitimise her activities, then that would be Gross Misconduct. For a civil servant that would be immediate dismissal...
I think you'd be unlikely to get much from the charities involved - what one person chooses to donate, whether on other people's behalf or not, is no business of anyone else, and unless you're in a position to represent your department officially, they would be very unlikely to tell you what donations have been received in your offices name.
Personally I don't understand the reluctance get involved - assuming it's genuine belief that money given to charity has been stolen then there is no moral problem with asking the appropriate authorities to investigate. If she's innocent then the investigation will last 10 minutes and she'll be exonerated, and your department will put in place rule regarding collections to ensure the same thing doesn't happen again - I'm surprised they don't, we do - if on the other hand she's been lifting several thousand a year from your colleagues pockets, then why would anyone object when she gets sacked and potentially prosecuted...?